A semi-classical picture of quantum scattering
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 2, pp. 149-183.
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     title = {A semi-classical picture of quantum scattering},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     url = {http://archive.numdam.org/articles/10.24033/asens.1738/}
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Nier, Francis. A semi-classical picture of quantum scattering. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 2, pp. 149-183. doi : 10.24033/asens.1738. http://archive.numdam.org/articles/10.24033/asens.1738/

[1] R. Abraham and J. E. Marsden, Foundation of Mechanics, Addison Wesley, 1985.

[2] W. O. Amrein, J. M. Jauch and K. B. Sinha, Scattering Theory in Quantum Mechanics, W. A. Benjamin, 1977. | MR | Zbl

[3] F. A. Berezin and M. A. Shubin, The Schrödinger Equation, volume 66 of Mathematics and its Applications, Kluwer Academic Publishers, 1991. | MR | Zbl

[4] J. M. Bony, Second Microlocalization and Propagation of Singularities for Semi-linear Hyperbolic Equations (Hyperbolic Equations and Related Topics, Mizohata ed. Kinokuya, 1986, pp. 11-49). | MR | Zbl

[5] J. M. Bony and J. Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander (Bull. Soc. Math. France, 1994, pp. 77-118). | Numdam | MR | Zbl

[6] J. M. Bony and N. Lerner, Quantification asymptotique et microlocalisation d'ordre supérieur I (Ann. Scient. Ec. Norm. Sup., 4e série, Vol. 22, 1989, pp. 377-433). | Numdam | MR | Zbl

[7] O. Bratelli and D. Robinson, Operator Algebras and Quantum Statistical Physics, Springer-Verlag, 1979-1981.

[8] C. Cohen-Tannoudji, B. Diu and F. Laloë, Mécanique Quantique, Hermann, 1973.

[9] P. Deift and E. Trubowitz, Inverse Scattering on the Line (Comm. on Pure and Applied Math., Vol. 32, 1979, pp. 121-251). | MR | Zbl

[10] J. Derezinski and C. Gérard, Asymptotic Completeness of N-Particles Systems, Springer Verlag, to appear.

[11] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, 1964. | MR | Zbl

[12] J. D. Dollard, Scattering into Cones 1 : Potential Scattering (Commun. in Math. Phys., Vol. 12, 1969, pp. 193-203).

[13] J. J. Duistermaat, Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities (Comm. on Pure and Applied Math., Vol. 27, 1974, pp. 207-281). | MR | Zbl

[14] M. V. Fedoryuk and V. P. Maslov, Semi-Classical Approximation in Quantum Mechanics, Reidel Publishing Company, 1985.

[15] C. Fermanian-Kammerer, Équation de la chaleur et mesures semi-classiques, Thèse, Univ. Paris XI, 1994.

[16] P. Gérard, Mesures semi-classiques et ondes de Bloch (Séminaire EDPX 1990-1991, (16)). | Numdam | Zbl

[17] P. Gérard and E. Leichtnam, Ergodic Properties of Eigenfunctions for the Dirichlet Problem (Duke Math. J., Vol. 71 (2), 1993, pp. 559-607). | MR | Zbl

[18] B. Helffer, A. Martinez and D. Robert, Ergodicité et limite semi-classique (Commun. in Math. Phys., Vol. 109, 1987, pp. 313-326). | MR | Zbl

[19] B. Helffer and J. Sjöstrand, Équation de Harper (Lect. Notes in Physics, Vol. 345, 1989, pp. 118-197). | Zbl

[20] L. Hörmander, The Analysis of Linear Partial Differential Operators, volume 3, Springer Verlag, 1985. | Zbl

[21] H. Isozaki and H. Kitada, A Remark on the Microlocal Resolvent Estimates for Two-Body Schrödinger Operators (RIMS Kyoto University, 1985). | Zbl

[22] H. Isozaki and H. Kitada, Scattering Matrices for Two-Body Schrödinger Operators (Sci. Papers College Arts Sci. Univ. Tokyo, Vol. 35, 1985, pp. 81-107). | MR | Zbl

[23] P. L. Lions and T. Paul, Sur les mesures de Wigner (Rev. Mat. Iberoamericana, Vol. 9 (3), 1993, pp. 553-618). | MR | Zbl

[24] A. Messiah, Mécanique Quantique, Dunod, 1965.

[25] F. Nier, Schrödinger-Poisson Systems in dimension d ≤ 3 : the whole space case (Proc. Roy. Soc. Edin., Vol. 123 A, 1993, pp. 1179-1201). | MR | Zbl

[26] F. Nier, Asymptotic Analysis of a Scaled Wigner Equation (Transp. Theory Stat. Phys., Vol. 24 (4-5), 1995, pp. 591-628). | MR | Zbl

[27] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Acad. Press, 1975.

[28] D. Robert, Autour de l'approximation semi-classique, volume 68 of Progress in Mathematics, Birkhaüser, 1987. | MR | Zbl

[29] W. Thirring, Quantum Mechanics of Atoms and Molecules, volume 3 of A Course in Mathematical Physics, Springer-Verlag, 1979. | Zbl

[30] X. P. Wang, Time-Delay Operators in the Semi-classical Limit. II. Short-range Potentials (Trans. Am. Math. Soc., Vol. 322(1), 1990, pp. 395-415). | Zbl

[31] K. Yosida, Functional Analysis, volume 123 of Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Springer-Verlag, 1968. | MR | Zbl

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